A STUDY ON THE CHAOS MODEL OF LIQUIDITY IN STOCK MARKET

For a Stock Market, the critical problem is the maintenance of its liquidity. Market liquidity can be described in various ways, in particular, in terms of the bid/offer spread and the market depth. Model of market liquidity dynamics has been proposed in Schmidt, A.B.' literate. In our study, we improve his model. On one hand, we think that trading volume is determined by the total number of traders, as well as the relations between the numbers of buyers and sellers, while the model of Schmidt only considers the first, item. On the other hand, Schmidt assumes that the number of "newcomers" in the market is in proportion to the current number of trades. However, we all know that the continual rise or fall of the price will also attract more buyers or sellers, that, is, "newcomers", into the market, which he has not taken for granted. We also prove it, to be a chaos model through analysis of Lyapunov exponent. On the assumption that price variation can be neglected, we discuss the conditions in which chao     

准坐标系下的弹性飞行器飞行动力学建模

结合有限元思想和拉格朗日方程推导了准坐标系下的弹性飞行器飞行动力学模型,与通常采用的平均轴系建模方法相比,该方法克服了变量难在相同坐标系下表示等缺点,而且该模型包含了自由度之间所有的耦合,能够更充分的反映刚性自由度与弹性自由度间的交叉耦合特性,更全面的从本质上体现飞行器结构动力学、空气动力学以及飞行动力学这种多学科之间相互影响的非线性飞行动力学特性。该动力学模型可用于弹性飞行器非线性稳定性分析、弹性飞行器飞行动力学与控制理论分析等。

Abstract：

As the frequency separation between the rigid body modes and the structural dynamics becomes tighter, the traditional aircraft flight mechanics treatment, there is, the rigid body approximation, may be not efficient. A complete coupled equation of motion for fully flexible aircrafts were derived, without any constraint relationship, which was done by employing Lagrange’s equations and the finite element method in terms of quasi-coordinates. This model includes automatically all six rigid-body degrees of freedom and elastic deformations, as well as the gravity, propulsion, aerodynamics, and control forces, in addition to forces of an external nature, such as gusts. Different from the modeling method based on ＂mean axes＂ coordinate system, the seamless integration was achieved by using the same reference frame and the same variables to describe the aircraft motions and the force acting on it, including the aerodynamic forces. The formulation is modular in nature, in the sense that the structural model, the aerodynamic theory, and the controls method can be replaced by any other ones to better suit different types of aircraft, provided certain criteria are satisfied.     

Study on Chaos Created by Hopf Bifurcation of One Kind of Financial System and Its Application

From a mathematical model of one kind complicated financial system, corresponding local topological structures of such kind system on condition of certain parametercombination, unstable equilibrium point of the system, conditions on which Hopf bifurcation is created and stability of the limit circle corresponding to the Hopf bifurcation as well as condition on which the limit circle is stable have been studied. From relationship between each parameter and the Hopf bifurcation all the way to route which leads to chaos etc have been studied. Following the above, conditions on which complicated behaviors created locally in such kind system has been analyzed. By applying fractal dimension, Lyapunov index, the intrinsic complexity of the system on such condition has been studied, and result of the numerical simulation proves the theory of this paper correct.     

Intelligent control over chaos in the rolling process and its comparison with tracking control

Some existing methods for chaos control in engineering fields are analyzed and their drawbacks are pointed out. A tracking method can solve these problems to some extent, but it still depends on the mathematical model of the system to be controlled. An intelligent method based on fuzzy neural network (FNN) is used to control chaos in engineering fields. The FNN is employed to learn the inherent dynamics from the input and output of chaos, which can be used in the inverse system method, so that the method is free of the exact mathematical model of the system to be controlled. This intelligent method is compared with tracking method in the presence of measurement noise and model error. Simulation results show its superiority and feasibility.     

Analysis of effect factors-based stochastic network planning model

Looking at all the indeterminate factors as a whole and regarding activity durations as independent random variables, the traditional stochastic network planning models ignore the inevitable relationship and dependence among activity durations when more than one activity is possibly affected by the same indeterminate factors. On this basis of analysis of indeterminate effect factors of durations, the effect factors-based stochastic network planning （EFBSNP） model is proposed, which emphasizes on the effects of not only logistic and organizational relationships, but also the dependent relationships, due to indeterminate factors among activity durations on the project period. By virtue of indeterminate factor analysis the model extracts and describes the quantitatively indeterminate effect factors, and then takes into account the indeterminate factors effect schedule by using the Monte Carlo simulation technique. The method is flexible enough to deal with effect factors and is coincident with practice. A software has been developed to simplify the model-based calculation, in VisualStudio.NET language. Finally, a case study is included to demonstrate the applicability of the proposed model and comparison is made with some advantages over the existing models.     

Preparation of entanglement states in a two-spin system by Lyapunov-based method

A stable Lyapunov-based control law is proposed for entanglement states preparation in this paper.The mathematical model of a two-spin system is constructed in interaction picture.An average value of observable operator is selected as the Lyapunov function.This paper designs the observable operator to make sure that the target state is stable in Lyapunov sense.Then the authors analyze the convergence of the control system,and demonstrate that the Bell states are asymptotically stable under the control law designed.Compared with other methods,the control method proposed in this paper has the advantages of easy design and convergence to the target states.Numerical simulation experiments for the preparation of Bell states are implemented.     

基于自适应观测器和自抗扰控制的PMSM直接转矩控制

提出一种新的自适应观测器,用于永磁同步电机直接转矩控制系统的定子磁链和定子电阻估计。该观测器利用静止坐标系下的电压模型估计定子磁链,采用转子坐标系下的电流模型估计定子电流,把定子电流估计误差通过增益矩阵作为反馈信号。定子电阻自适应律根据李亚普诺夫稳定性理论推出,观测器的增益矩阵采用极点配置方法得到,观测器的收敛性根据李亚普诺夫稳定性分析来保证。此外,采用自抗扰控制技术设计了速度控制器,该控制器能对负载扰动进行估计和补偿。仿真结果证明了所提自适应观测器的有效性和自抗扰控制器的抗负载扰动能力。

Abstract：

A new adaptive observer was proposed to estimate the stator flux and stator resistance in the direct torque controlled permanent magnet synchronous motor （PMSM） drive. The stator flux was estimated by using the motor voltage model in the stationary frame, and the stator currents were estimated by using the motor current model in the rotor frame. The current estimation errors were then used as feedback signals through a gain matrix. Stator resistance adaptive law was developed based on Lyapunov stability theory. The observer gain matrix was obtained by using the pole placement method. The stability of the adaptive observer was guaranteed by the Lyapunov stability analysis. In addition, a speed controller was designed based on active disturbance rejection control （ADRC） technique to estimate and compensate the load disturbance. Simulation results have confirmed both the effectiveness of the adaptive observer and the anti-load-disturbance performance of the active disturbance rejection controller.     

电力关键基础设施网络仿真模型研究

电力网络模型是关键基础设施模型中的重要组成部分。分析了现实电力网络的拓扑结构和运行原理,根据复杂网络的基本理论,采用基于Agent的建模方法设计实现了关键基础设施中电力网络模型。通过仿真实验,较好的模拟了电力系统输送电能的动态过程和因偶发故障而造成的大规模停电现象,对复杂电力网络的动力学特性进行了初步探索。

Abstract：

The model of electric power network is a major part of critical infrastructure model. The topology of network structure and the principle of net function were analyzed, according to the theory of complex network, applying the agent-based modeling to design and realize the model of electric power network. Through the simulation experiment, it was demonstrated to be better ways to simulate the dynamic progress of electric transmission and the cascading failure phenomenon caused by incidental trouble. The simulation model offers an effective approach to analysis electric power network’s role in critical infrastructure, and makes a step to exploration for complex electric power network’s dynamic character.     

单线列车运行调整的梯度搜索算法仿真与研究

列车运行调整的优化是一个非常复杂的问题,需考虑的因素很多,很难给出一个完美的优化模型。根据单线列车运行调整的特点,建立了单线列车运行图的离散事件拓扑图模型,提出了＂调整运行图综合满意度＂作为运行调整的目标,并进一步论证了＂调整运行图综合满意度＂函数的单调递减特性;提出了冲突树的概念和梯度搜索算法的算法原理及搜索步骤,并实例进行仿真。仿真结果表明,该算法模型在实际运行过程中的具有较好的优化性和有效性。

Abstract：

The optimization of railway rescheduling is a very complex issue, many factors should to be taken into account, and it’s difficult to give a perfect optimization model. A discrete event topologic diagram model was derived according to the characteristics of the single-track railway diagram, and the ＂comprehensive satisfaction of the adjusted train diagram＂ was proposed as the target of the railway rescheduling, then the monotonically decreasing characteristic of the target function was demonstrated. The concept of conflict tree was developed and the principle and steps of the gradient search algorithm based on the DET model were given and simulated. The simulation results show that this algorithm has better adaptability and effectiveness in practical application.     

装甲装备月份维修计划优化制订方法研究

分析装甲装备月份维修计划的制订目前存在的问题,通过研究任务与装甲装备月份维修计划之间的相关关系,提出了根据任务的强度确定维修时机为优化目标的维修计划优化模型,统筹考虑维修资源、规章制度等因素。经LINGO软件仿真验证,结果显示该模型能够极大化装备的使用效益,实现科学化、精确化的送修,以及对装备的集约化管理。

Abstract：

The problems were analyzed that lay in the formulation of the armored equipment month maintenance plan. Based on researches about the relationship between the mission and the month maintenance plan, a maintenance plan optimization formulation model was brought forward. The model took factors such as maintenance resources, rules and regulations into overall consideration, and selected maintenance opportunity based on the strength of the mission as optimization goal. The model was validated by LINGO simulation. The result shows that the model can not only maximize the use efficiency, but also realize the scientific and precise delivery and the intensive management of the equipment which needs preventive maintenance.     

对中小学课程难度灰色模型GMg(1, 1)的探索

本文依据课程难度的标准是学生发展的动态水平的原理, 首先验证了儿童青少年的心理发展与大脑发育之间存在异步正相关规律, 而且相关程度极高, 然后以儿童脑电频率数据作为心理发展的映射量建立起了由低值模型、均值模型和高值模型组成的中小学课程难度的灰色模型体系。     

SDN子网进化博弈研究

基于replicator dynamics(RD)模型的构建思想,提出了SDN(supply and demand network with mul-tifunction and opening characteristics for enterprise)子网的进化博弈模型,进而构造出了合作博弈策略混沌演化的数学模型。在RD模型的局部稳定点分析基础上,利用该数学模型生成了合作博弈的混沌演化模拟图,通过博弈的混沌演化模拟,从混沌演化的角度深入探讨了ESS的动态形成过程,佐证了SDN子网的混沌演化规律,验证了不同博弈阶段的子网结构也同样经历混沌的演化过程。这有助于预测SDN及其子网中群体行为的变化趋势,同时对进化博弈理论的动态研究也有一定的参考价值。     

一类量本利模型的混沌表现评价

首先对一个产出博弈模型进行拓展,并导出一种量本利模型.然后利用商业和会计文献中的经济指标对该模型的混沌表现进行评价,把1维情形下的混沌表现评价推广到参与人之间存在博弈的2维情形,为下一步模型的混沌控制提供依据.并用数值方法求出了以不同的评价指标作为参与人收益时的Nash均衡点.并对各种经济指标下系统进入混沌态后的表现进行对比.     

发电市场不同决策规则三寡头博弈模型研究

在三寡头垄断的电力市场中假设生产者分别采用静态预期及有限理性预期规则,建立了一个基于不同决策规则的动态博弈模型.对该模型进行了较详细的理论分析和参数仿真计算,在一定范围内得出了系统出现混沌的参数值,分析了不同参数组合条件下系统表现出来的分岔,混沌和密度周期性等复杂性态.所得结果对于一般寡头电力市场中的生产者制定产量计划具有一定启示作用.     

BOOST变换器中混沌现象及其控制的仿真研究

分析了工作在电流断续状态下BOOST变换器的离散迭代模型,对该迭代模型的分岔现象进行了仿真研究。基于MATLAB的POWER SYSTEM工具箱,采用基于器件模型的仿真研究证实了该变换器中的混沌现象。针对该混沌现象采用了跟踪控制方法进行控制,该方法消除了变换器中的混沌现象,使变换器工作在周期1状态,基于迭代模型和器件模型的仿真结果表明了混沌现象的存在和所提控制方法的有效性。     

基于混沌遗传算法的板坯入库决策优化方法

针对热轧板坯库优化管理，分析了板坯入库操作流程，并建立了板坯入库决策的优化模型，考虑了板坯入库库位和垛位选择的多种原则，对一个板坯入库批次进行全局优化运算，可快速为板坯选择最优的库位和垛位。对于模型的求解方法，构造了一种自适应的混沌遗传算法，采用自然数编码方式，动态的在线调整算法的交叉和变异概率，并采用混沌优化方法作为变异算子。对生产数据进行实际排产的结果表明，建立的模型和算法切实可行，可应用于生产实际。     

基于混沌判据评价几类跟驰模型合理性的仿真研究

提出了一种评价交通流理论模型合理性的新方法:用交通流理论模型产生时间序列,计算这些时间序列的最大李雅普诺夫指数,用最大李雅普诺夫指数可以判断仿真交通流是否再现了交通流存在的混沌现象,以及反映的程度如何,进而评价交通流理论模型的合理性.文章介绍了方法的原理,给出了对伽赛斯-赫尔曼-伯兹(Gazis-Herman-Potts)模型;皮埃莱(Bierley)模型;洛克威尔-特莱德勒(Rock-well-Treiterer)模型三类典型的跟驰模型仿真实验的结果.分析了仿真结果,得出了有用的结论.     

一类混沌经济模型的直线控制法研究

就混沌经济系统中两种形式的直线控制法进行了讨论，一种形式的直线控制法是对控制参数进行扰动，另一种是加入外部控制信号对状态变量的取值进行调整，二者都不需要固定点存在稳定流形．以寡头市场条件下量本利模型的两类混沌态为例，分别用两种形式的控制方法成功、快速地将其控制到Nash均衡点．对实施控制前后企业的累计销售收入和累计利润进行对比中可看到，实施控制后企业的业绩有较大改善．对直线控制法在实践中如何运用进行了讨论．     

一类混沌广告模型的直线控制

将参数扰动直线控制法引入到双寡头有限理性广告博弈模型中，建立了双寡头广告直线控制模型。研究两种不同情况下企业对系统进行控制，一是在NASH均衡点附近时引入直线控制，另一种是在较远的点时引入直线控制。通过理论分析和数值模拟发现，初期控制成本和控制效果依赖于企业控制点的选择和增益矩阵k的取值，在同一个控制点，控制效果与k值密切相关。同时指出对于处于混沌状态的企业，应选择在两企业的广告投入量位于NASH均衡点附近或两侧时，进行控制，将能够取得比较好的控制效果。     

一类混沌经济模型的阈值控制法研究

把利用相空间压缩来控制混沌应用于经济系统,并针对经济系统的特点引申出阈值控制法,即通过限制变量取值的上限或(和)下限来达到控制混沌的目的.并以2维动态产量博弈模型为例,以一个参与人采取控制和两个参与人同时参与控制等形式,成功地实现了模型混沌态的控制.通过控制前后企业累计利润的对比,可看出控制后企业的业绩可得到较大改善.